(a) Mass of the automobile is given as $=3000 \mathrm{~kg}$

The suspension sags by a length of $15 \mathrm{~cm}$

Decrease in amplitude $=50 \%$ during one complete oscillation

If each spring’s spring constant is $k$, the spring constant of the four springs in parallel equals

$\mathrm{K}=4 \mathrm{k}$

Since $F=4 k x$

$\mathrm{Mg}=4 \mathrm{kx}$

$\Rightarrow k=M g / 4 x=(3000 \times 10) /(4 \times 0.15)=5 \times 10^{4} \mathrm{~N}$

(b) Each wheel supports $750 \mathrm{~kg}$ weight

$\mathrm{t}=2 \pi \sqrt{\mathrm{m}} / \sqrt{\mathrm{k}}=2 \times 3.14 \times\left(\sqrt{\left.750 / \sqrt{5} \times 10^{4}\right)}=0.77 \mathrm{sec}\right.$

Using, $x=x_{0} e^{-\frac{b t}{2 m}}$,

we get

$\frac{50}{100} x_{0}=x_{0} e^{-\frac{6 \times 0}{2 \times 75}}$

$\log _{e} 2=(b \times 0.77) /(1500) \log _{e} e$

$b=\frac{(1500) \log _{c} 2}{0.77}$

$\mathrm{b}=(1500 \times 0.6931) / 0.77=1350.2 \mathrm{~kg} / \mathrm{s}$